So long as the projector had an HDMI input (or you could get an appropriate HDMI -> DVI / VGA converter), the Apple TV (latest one) would do this I think? Should simply be just connect the ATV3 to the projector, then use Airplay Mirroring to send the iPad's display to the ATV3.

Not exactly a cheap solution I know, and you'd also have to have both the ATV3 and the iPad connected to a wireless network of some kind.

Can't think of anything other than an ATV I'm afraid. You can use a Mifi wireless dongle as a wireless hub (have done this in the past) but this is even more expense.

I used to connect my macbook to the projector, and use keynote remote on the iPhone to control it. The great thing about presenting this way, is you can keep bullet point reminders about your presentation structure on the phone, but many will not realise you are doing anything other than changing slides when you look down at it. Although keynote on iPad is ok, I find using it on the laptop and controlling with a separate device much more powerful.

Finally, the macbook can generate its own wireless access point to connect the iOS device to so you don't need to worry about wifi connections wherever you are presenting. Not ideal if you want to ditch the laptop however.

I connect the iPad to the projector (hardwire), & then use my ipod touch as a Keynote remote. I can see all the slides on my ipod touch & can change slides. Also, if I want to point towards a particular, err.. point on the slide, I long press on that area in my ipod touch, & a red laser pointer comes up on the presentation. My ipod touch connects to the iPad via Bluetooth.